Quasitriangularity of quantum groups at roots of 1

Details Quasitriangularity of quantum groups at roots of 1 Quasitriangularity of quantum groups at roots of 1

1994-03-18

arxiv.org/abs/hep-th/9403105v1

Commun.Math.Phys. 170 (1995) 79-100

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1007/BF02099440

An important property of a Hopf algebra is its quasitriangularity and it is useful various applications. This property is investigated for quantum groups $sl_2$ at roots of 1. It is shown that different forms of the quantum group $sl_2$ at roots of 1 are either quasitriangular or have similar structure which will be called autoquasitriangularity. In the most interesting cases this property means that "braiding automorphism" is a combination of some Poisson transformation and an adjoint transformation with certain element of the tensor square of the algebra.

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